I must ask... Why must you tell?

Approximately 2 times a week we have visitors in my 3rd grade classroom.  Other teachers come in to watch us do math and after my lesson with 3rd graders, I have the privilege to debrief with my colleagues and share some thoughts about what I'm learning from my 3rd graders.  This year has been an amazing journey, and I have learned so much from both my students and my peer observers. 

Last week, during one of these debriefing sessions, a teacher asked me this string of questions (I'm paraphrasing), "You don't really teach much do you?  I mean they teach each other, right?  You just guide their discussion by asking questions, right?"

Exactly!  You got it.  That's exactly what happens in my classroom.  The students teach.  I facilitate.  There has not been a single day of direct instruction for my third graders all year long.  By direct instruction I mean I have not stood up in front of the classroom and said here is a problem, and here is how you solve it. Nor have I said, we're going to learn about this concept today, here is what it means and this how you do it.  (Well there was that one day, when I accidentally modeled, read about it in my post "To model or not to model. That is the question.")

Yet my students are learning.  On a daily basis.  They learn from each other.  I pose a problem, or a task, they share their thinking and I ask them questions to refine their thinking.  We discuss and argue and discuss until we come to a consensus. I ask questions like:

How is your way different from hers?
Can you explain to the class what you meant by that?
Will you tell us what he helped you understand?
Can you repeat what she said?
Do you have something you would like to add?
Did you use a similar or different strategy?
Who can help us understand his thinking?
What do you think she meant when she said that?
Can you tell your shoulder partner which strategies convince you?
Has anyone's thinking changed?
Do you agree or disagree and why?
Why does that make sense?
Would you like to revise your thinking?
How can we help this mathematician be more precise?
What questions do you have for him?

With so much of the focus on my students and their thinking, it could be easy to assume that the discussions in my classroom are random and unpredictable.  That's not true though, because I do more than just ask questions.  I also listen.  I listen with a purpose.  Whatever task or problem I posed was posed with certain learning goal in mind and as I listen to my students discuss the task I listen for connections to be made.  I listen for key ideas and orient my students toward them.  I am the guide that helps the discussion reach its final destination.

If you're thinking you don't have time for discussions like this every day, then I have a challenge for you.  Just try one.  Try one day where you don't tell your students anything.  Do nothing but ask questions.  Just let go and let them.  I think you'll be amazed.

If you need some motivation to keep you going during this challenge, just listen to my new favorite song before you get started...

Let it go...

Oh, it's a number line!

I have a confession.  This post has been written and unwritten and rewritten many times.  It is the reason I have not written a blog post for an entire quarter.  This project was adapted from a combination of ideas from training sessions, math coaches and friends input.  It was fabulous, but nothing I have written about it has turned out to be as fabulous as it actually was when I did it in class.  I'm sharing anyway.  Hopefully, someone will glean something from it.  Here goes...

In my classroom I have a number line.  It's not any old number line.  It's different.  The first day my students saw my number line it looked like this:

On this day our number talk went something like this:

Do you notice anything new in our classroom? What do you notice about it?

There is a whiteboard, there is purple duct tape, there are three strings, there is an orange piece of paper, there are many rectangles.  

Tell me more about the string and the piece of orange paper.

The string is long, the paper is short, there is only one paper, there are three strings, the paper is folded over the string, the string is longer.

What do you mean the string is longer?  How do you know?

Because there is only one piece of paper, but there could be more.  More papers could fit on the string so that makes the string longer than the paper.

How many papers could fit on the string?

End day one.  Day 2 picked up with that very question, "How many orange papers of the same size could fit on one of the strings?  First I took guesses from the students, there was a wide range, then I allowed them time to try different measurement techniques.  Some students tried finding other objects that were the same size to lay across the floor, some tried what I like to call "air measuring" with their fingers and their eyes (that was fun because we got all sorts of different "reasonable" answers), some tried moving the paper and marking the white board.  After a discussion about what technique seemed to be the most accurate and precise, I "accidentally" dropped my folder which contained many more orange papers.  One of my students immediately had the idea that we could just place more orange papers on the string to find out how many would fit.  So we did.  It looked like this:

Ten orange papers could fit.  I asked the students,

How many units wide do you think one of the orange papers is?  

They looked confused.  5? Maybe 10? Could be 1,000,000!

Oh wait, I forgot something:

Oh, it's a number line!  

After some guesses, and some skip counting and some discussion, we finally figured out that each piece of paper must be 100 units.  So we labeled them and it looked like this:

The next day our discussion started with this question:

If there are 10 hundreds in 1,000, then how many tens are in 1,000?

Our discussion ended with this:

On day four I asked the students if they could write a number sentence to represent the orange pieces of paper.  We had a fabulous number talk revolving around equivalent number sentences and equality.  Ultimately, one of my students very excitedly suggested 10 x 10 x 10 and we modified our number line to look like this:

The number line still lives in my classroom and we have referenced it several times.  We've used it for rounding, grouping, division and much more.  Soon I will remove the original papers and the number line will be used for fractions.  I can't wait!

One more confession:  It took me three tries to build a number line that could survive in a classroom of 3rd graders.  On my first attempt I used string.  It sagged the top row of papers overlapped the middle row.  It was ugly, I took it down and tried again.  My second attempt was using 20 gauge wire.  Extremely pliable.  It also sagged, and broke easily.  The kids bumped it with their knees and the wire fell many times.  This third attempt was built with 16 gauge wire.  Not as easy to work with but much sturdier.  I also used flat head nails hammered into the shelving unit through the shower board to hold the wire in place.  I think this number line will last through the remainder of the school year.